SANTA CLARA, Calif. — After losing his top two running backs to injuries in the span of a few days, San Francisco 49ers coach Kyle Shanahan is turning to a familiar face to provide some much-needed depth.

Shanahan announced Monday that the Niners intend to sign veteran running back Alfred Morris in the next couple of days, pending Morris’ ability to pass a physical. Morris is slated to meet the Niners in Houston, where the team will have joint practices this week against the Texans before Saturday’s preseason game.

San Francisco 49ers running back Jerick McKinnon underwent an MRI on Sunday that revealed a strained calf muscle, according to a team spokesman.

Morris’ familiarity with Shanahan dates to the two years they spent together with the Washington Redskins when Shanahan was offensive coordinator there in 2012 and 2013. Those were also Morris’ two most productive NFL seasons, rushing for 1,613 yards and 13 touchdowns in 2012 and 1,275 yards and seven touchdowns in 2013.

From a scheme standpoint, Morris shouldn’t have too much of an adjustment to the zone-heavy philosophy Shanahan prefers.

“Alf did a great job for us for the two years I was with him,” Shanahan said. “It’s not flashy but he runs extremely hard, he’s very reliable, he’s a hard-nosed runner you can keep handing the ball off to.”

The need for help at running back was created by recent injuries to starter Jerick McKinnon and top backup Matt Breida. McKinnon suffered a calf strain in Sunday’s practice and will sit out this week before being re-evaluated next week. Breida sustained a separated shoulder in Thursday’s preseason game and will miss the rest of the preseason. He’s expected to be ready to go for the season opener Sept. 9 against the Minnesota Vikings.

Alfred Morris flourished with the Redskins in 2012 and 2013 when now-49ers head coach Kyle Shanahan was his offensive coordinator. Brad Mills/USA TODAY Sports

Joe Williams, who missed Sunday and Monday practices to attend to a death in the family, is expected to rejoin the team in Houston. If Morris’ signing goes through, the Niners would have a group of Williams, Morris, Raheem Mostert, Jeremy McNichols and Jeff Wilson Jr. to participate in the joint practices and preseason game against the Texans.

Morris, 29, is a six-year veteran who spent the past two seasons with the Dallas Cowboys. Shanahan said he had previously considered bringing Morris on board but didn’t want to make the move until he thought Morris would be in a position where he’d have a legitimate chance to make the 53-man roster.

“I just told him I waited so long to invite him because I wouldn’t invite him unless I believed he had the chance to make the team,” Shanahan said. “I do believe he has a chance to make the team here. And that’s all Alf wants. He wants a chance to compete.

“I think with some of these injuries that we’ve had now he does have a chance to compete. He’s getting in late but we’ll see how he does over these next few weeks and if he’s running the same way he always has, he’ll have a chance.”